there are all sorts of features in the behavior of these rules that could in principle represent a possible purpose. But what is special about rules like those on the previous page is that they are the minimal ones that exhibit the particular feature of doubling their input.

And in general if one sees some feature in the behavior of a system then finding out that the rule for the system is the minimal or optimal one for producing that feature may make it seem more likely that at least with sufficiently advanced technology the system might have specifically been created for the purpose of exhibiting that feature.

Computational irreducibility implies that it can be arbitrarily difficult to find minimal or optimal rules. Yet given any procedure for trying to do this it is certainly always possible that the procedure could just occur in nature without any purpose or intelligence being involved.

And in fact one might consider this not all that unlikely for the kind of fairly straightforward exhaustive searches that I ended up using to find the cellular automaton rules in the pictures on the previous page.

So what does all this mean for extraterrestrial intelligence?

Extrapolating from our own development we might expect that given sufficiently advanced technology it would be almost inevitable for artifacts to be constructed on an astronomical scale—perhaps for example giant machines with objects like stars as components.

Yet we do not believe that we have ever seen any such artifacts.

But how do we know for sure? For certainly our astronomical observations have revealed all sorts of phenomena for which we do not yet have any very satisfactory explanations. And indeed until just a few centuries ago most such unexplained phenomena would routinely have been attributed to some kind of divine intelligence.

But in more recent times it has become almost universally assumed that they must instead be the result of physical processes in which nothing like intelligence is involved.

Yet what the discoveries in this book have shown is that even such physical processes can often correspond to computations that are at least as sophisticated as any that we as humans perform.

But what we believe is that somehow none of the phenomena we see have any sense of purpose analogous to typical human artifacts.